Suppose an individual faces employment risk

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Suppose an individual faces employment risk of the following form: Her employment is subject to business cycles in which she faces the risk of a layoff with probability 10%. When she is employed, she receives an income of $100. She earns nothing when she is laid-off. Suppose her utility over consumption in the states of the world when she is employed (xE ) and when she is unemployed (xU ) is given by 1 1 U (c0, c1) = (0.9)(xE ) 2 + (xU ) 2 . (3) Assume that there exists employment insurance which provides support in the event that she finds herself unemployed. Specifically, for each unit of insurance she purchases at a price p she will receive one unit of consumption in the event of a layoff. (a) Graph this individual’s possible consumption choices with xE on the horizontal axis and xU on the vertical axis. Include the equation for her budget line and a hypothetical indifference curve through her endowment point. (b) Calculate the individual’s certainty equivalent to her endowment. (c) Write out the two conditions that will hold at the individual’s optimal insurance decisions. Provide an explanation of each. (d) Suppose that p = 0.10. Calculate the individual’s optimal consumption decision. From this, derive her optimal insurance purchase. (e) Suppose that p = 0.20. Calculate the individual’s optimal consumption decision. From this, derive her optimal insurance purchase. Suppose the employment insurance is actuarially fair. Explain what this means. What does this imply about the price of insurance p? Do you think employment insurance?

Reference no: EM131009702

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